A Model for the Tear Film and Ocular Surface Temperature for Partial Blinks

Abstract

In this paper, we investigate the dynamics of tear film and the associated temperature variation for partial blinks. We investigate the mechanism of fluid supply during partial blink cycles, and compare the film thickness with observation in vivo. We find that varying the thickness of the fluid layer beneath the moving upper lid improves the agreement for the in vivo measurement of tear film thickness after a half blink. By examining the flux of the fluid, we provide an explanation of this assumption. We also investigate the temperature dynamics both at the ocular surface and inside the simulated anterior chamber. Our simulation results suggest that the ocular surface temperature readjusts rapidly to normal temperature distribution after partial blinks.

Thermal analysis of dry eye subjects and the thermal impulse perturbation model of ocular surface

“…The lens has a significantly lower thermal conductivity than that of the surrounding aqueous humor and vitreous humor (Lagendijk, 1982;Scott, 1988); therefore the lens will hinder any rapid heat flow through this region. Only the anterior part of the cornea will experience relatively sharp temperature change due to the perturbation of a blink, which is also demonstrated in the model by Deng et al (Deng et al, 2013, 2014.…”

“…Even for t ¼ 0.01 s, the measurable anterior corneal layer is already larger than 34.7 C. The rapid warming by the eyelid in our first-order model is faster than what physically happens since we assumed the eyelid will cover the entire eye immediately at the start of a blink, which ignores the eyelid down-stroke and up-stroke movement. A more realistic eyelid movement model has been analyzed (Deng et al, 2013(Deng et al, , 2014. Nonetheless, our model still demonstrates that the movement of the eyelids is the limiting factor of the thermal pulse effect, and the anterior corneal temperature will rise rapidly, once the eyelids are covering the cornea.…”

“…Later Li and Braun (Li and Braun, 2012) developed a sophisticated mathematical model of the ocular surface cooling process and were able to fit their results to experimental data. Extended from Li and Braun's model, the dynamics of temperature field during and after partial blinks and multiple blink cycles has been studied recently (Deng et al, 2013(Deng et al, , 2014.…”

Calculation of the heat flux near the liquid–gas–solid contact line

“…The essence of this method is that the initial Cauchy problem (1)-(4) was reformulated as the inverse problem by the search for unknown boundary condition λτ y | z=h , if the additional information is known τ | z=0 = τ 0 (x, y) (11) concerning the solution to the direct problem div λ∇τ = −q V , (x, y, z) ∈ V, (12) λ τ x| x=0 = 0, λ τ x| x=A = 0, λ τ y| y=0 = 0, λ τ y| y=B = 0, (13) λ τ z| z=0 = α τ | z=0 , λτ z | z=h = −Q(x, y). (14) Direct problem (12)- (14) is well posed.…”

“…The problem of determining the rate of evaporation and heat flux density in the heated liquid near the three-phase contact line is actively investigated in connection with important practical applications in power engineering, medicine, chemical, pharmaceutical and food industry [11][12][13]. Both theoretical and experimental studies suggest that heat transfer intensity near the contact line can be more than an order higher than the average one, and it causes a local temperature minimum on the solid wall.…”